Question

What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is -2.18 x 10^-11 ergs

Answer 1

Energy of electron in nth orbit of H atom is given by

= {-2.18 x 10^-11 ergs}/{n²}

Thus, E₁ = -2.18 x 10^-11 ergs

= -218 x 10^-13 ergs

and E_s = {-2.18 x 10^-11}/{(5)²} ergs

= -8.72 x 10^-13 ergs

Energy required for the electronic transition

ΔE = E₅ - E₁

= -8.72 x 10^-13 ergs - (-218 x 10^-13 erg)

= 2.08 x 10^-11 ergs

Wavelength of the emitted radiation,

λ = ch/ΔE = {3 x 10¹⁰ cm x 6.626 x 10^-27 ergs}/{2.09 x 10^-11 ergs}

or, λ = 9.511 x 10^-6 cm

= 951.1 x 10^-8 cm = 956 Å